Proximal point algorithm involving fixed point of nonexpansive mapping in 𝑝-uniformly convex metric space
2019 ◽
Vol 10
(4)
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pp. 437-446
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Keyword(s):
AbstractWe prove some important properties of the p-resolvent mapping recently introduced by B. J. Choi and U. C. Ji, The proximal point algorithm in uniformly convex metric spaces, Commun. Korean Math. Soc. 31 2016, 4, 845–855, in p-uniformly convex metric space. Furthermore, we introduce a modified Mann-type PPA involving nonexpansive mapping and prove that the sequence generated by the algorithm converges to a common solution of a finite family of minimization problems, which is also a fixed point of a nonexpansive mapping in the framework of a complete p-uniformly convex metric space.
2018 ◽
Vol 23
(5)
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pp. 664-690
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